I think one of the key points comes at the very end: teaching algorithms becomes rote learning _if the teacher does not understand the underlying mathematics in

I think one of the key points comes at the very end: teaching algorithms becomes rote learning _if the teacher does not understand the underlying mathematics in depth_. I wonder how many of the teachers who advocate for "visual" learning instead of algorithms are doing so because otherwise they'd have to admit they couldn't explain why the algorithm works themselves?